Areas Related to Circles Class 10 Mathematics — Revision Notes
This chapter deals with calculating areas of circles, sectors, and segments. These concepts are essential in geometry and have practical applications in de
TL;DR: This chapter deals with calculating areas of circles, sectors, and segments. These concepts are essential in geometry and have practical applications…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
This chapter deals with calculating areas of circles, sectors, and segments. These concepts are essential in geometry and have practical applications in de
Area and Circumference of Circle
- Circumference of circle equals 2 pi r where r is radius
- Area of circle equals pi r squared
- Diameter is twice the radius
- Pi is approximately 22/7 or 3.14159
- Circumference equals pi times diameter
Sector of a Circle
- Sector is a region of circle between two radii and an arc
- Area of sector equals (theta/360) times pi r squared
- Arc length equals (theta/360) times 2 pi r
- theta is the angle of sector in degrees at the center
- Semi-circle is a sector with angle 180 degrees
Segment of a Circle
- Segment is region between a chord and arc of circle
- Area of segment equals area of sector minus area of triangle
- Minor segment is smaller; major segment is larger
- For calculation, need to find area of sector and triangle separately
- Triangle is formed by two radii and the chord
Combination of Figures
- Problems often combine circles with other shapes like rectangles and triangles
- Find areas of individual shapes and add or subtract appropriately
- Shaded regions require careful identification of component areas
- Many practical problems involve finding area of combined figures
- Sketching helps in understanding and solving complex problems
Practical Applications
- Pizza size comparison uses area of circular sectors
- Clock problems involve calculating angle and arc length
- Garden design uses circular paths and flower beds
- Athletic tracks are oval with circular curves
- Gear design in machinery uses circular segments
Key Terms
- Sector: Region of circle bounded by two radii and an arc
- Segment: Region of circle bounded by a chord and an arc
- Arc Length: Distance along the circumference between two points on circle
- Chord: Line segment joining two points on a circle
Frequently Asked Questions
What is the area of a semi-circle with radius 7?
The area of a semi-circle equals half the area of a full circle. Area equals (1/2) times pi times 7 squared equals (1/2) times pi times 49 equals 24.5 pi or approximately 77 square units.
How do you find the area of a segment if you know the radius and central angle?
Calculate the area of the sector using (theta/360) times pi r squared. Then calculate the area of the triangle formed by two radii using (1/2) times r squared times sin(theta). Subtract triangle from sector to get segment area.
More Class 10 Mathematics Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
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